A SIMULATION STUDY OF THE LM-2500GAS TURBINE ENGINE INVENTORY SYSTEM
John Scott Cushing
NAVAL POSTGRADUATE SCHOOL
Monterey, California
THESISA SIMULATION STUDY OF THE LM-2500GAS TURBINE ENGINE INVENTORY SYSTEM
by
John Scott CushingWilliam Kirten Gautier
andDouglas Allen Long
Thesis Advisor:Thesis Advisor:
J. K. HartmanA. R. Washburn
MAR 1972
Approved faok pubtic h.oJLQji&<i; dii>txlbuutioYi untlmltcd.
A Simulation Study of the LM-2500Gas Turbine Engine Inventory System
by
John Scott pushingLieutenant, United States Navy
B.S., United States Naval Academy, 1964
William Kirten GautierLieutenant, United States Navy
B.S., United States Naval Academy, 1967
Douglas Allen LongLieutenant, Supply Corps, United States Navy
B.A. , Kalamazoo College, 1963
Submitted in partial fulfillment of therequirements for the degree of
MASTER OF SCIENCE IN OPERATIONS RESEARCH
from the
NAVAL POSTGRADUATE SCHOOLMarch 197 2
.
ABSTRACT
LM-2500 gas turbine engine rotable pool requirements
were studied using computer simulation. System operating
characteristics were observed with various scenarios and
management philosophies. Several purchase plans were
formulated and tested once system trends were established.
From this information, cost-effectiveness relationships
were derived.
Best estimates of system variables indicated that cost-
effectiveness was optimized for a rework capacity of seven
to eight engines and the purchase of fourteen to sixteen
engines early in system life as rotable pool spares.
TABLE OF CONTENTS
I. INTRODUCTION 9
II. NATURE OF THE PROBLEM .......... 11
A. GENERAL 11
B. ASSUMPTIONS 14
III. THE MODEL 17
A. REASONS FOR SIMULATION 17
B. MODEL DESIGN 17
C. GENERAL DESCRIPTION 18
1. GPSS Section 18
2. FORTRAN Section 18
D. OPTIONS OF THE MODEL 19
1. Option 1 19
2. Option 1 With Patrol Frigate
Program 20
3. Management Options 20
4. Purchase Plan Options 21
5. Split Rotable Pool Option .... 21
E. MODEL OPERATION 21
F. LEVEL OF DETAIL 22
IV. PRESENTATION AND ANALYSIS OF DATA .... 24
A. SELECTRION OF THE BASE CASE 24
1. Fleet Operating Profile 24
2. Time Between Overhaul (TBO) ... 24
3. Rework Time 24
4. System Transit Time 24
5. Probability of a Random
Failure 26
6. Rework Capacity 26
B. NATURE OF RESULTS 27
C. EFFECT OF CONSTANT TBO ' S 30
D. EFFECT OF TBO GROWTH 34
E. EFFECT OF REWORK TIMES 38
F. EFFECT OF RANDOM FAILURES 38
G. EFFECT OF SYSTEM TRANSPORTATION TIME . . 41
H. EFFECT OF PF PROGRAM AND REWORK
FACILITY CAPACITIES 41
I. EFFECT OF MANAGEMENT OPTION 44
J. BASE CASE ENGINE REQUIREMENTS 44
K. EFFECTS OF VARIOUS PURCHASE PLANS ... 50
V. CONCLUSIONS 57
VI. RECOMMENDATIONS 59
APPENDIX A DISTRIBUTION OF TIMES BETWEEN
SCHEDULED OVERHAULS 60
APPENDIX B COSTING INFORMATION 66
APPENDIX C RELIABILITY CONSIDERATIONS 69
APPENDIX D NORMALITY OF RUNS 72
APPENDIX E DETAILED MODEL DESCRIPTION 73
A. CONTROL INFORMATION 73
B. ACCUMULATION OF STATISTICS .... 74
C. INDIVIDUAL BLOCK DESCRIPTIONS . . 74
D. SUPPORTING FORTRAN SUBROUTINES . . 74
APPENDIX F ACCURACY OF THE MODEL 75
APPENDIX G FLOWCHARTS OF THE MODEL 76
COMPUTER PROGRAMS 83
LIST OF REFERENCES 106
INITIAL DISTRIBUTION LIST 10 7
FORM DD 1473 109
LIST OF TABLES
I. ENGINE REQUIREMENTS AT VARIOUS TBO '
S
AND OPERATING TEMPOS 4 8
II. ENGINE REQUIREMENTS AT VARIOUS TBO
SCHEDULES AND OPERATING TEMPOS 49
III. RESULTS OF PURCHASE PLAN TESTS 51
IV. RESULTS OF PURCHASE PLAN TESTS WITH
VARIOUS REWORK FACILITY CAPACITIES 55
C-I. FAILURE FREQUENCIES FOR CRITICAL
COMPONENTS 70
C-II. EARLY FAILURE PROBABILITIES 70
LIST OF FIGURES
1. ENGINE FLOW PATHS 12
2. TBO GROWTH 25
3. ENGINE MEAN OVERHAUL TIME 26
4. BASE CASE RESULTS 28
5. EFFECT OF RANDOM NUMBER CHANGE 29
6. EFFECT OF TBO CHANGE 31
7. EFFECT OF TBO CHANGE 32
8. EFFECT OF TBO CHANGE 33
9. EFFECT OF TBO FUNCTION CHANGE 35
10. EFFECT OF TBO FUNCTION CHANGE 36
11. EFFECT OF TBO FUNCTION CHANGE 37
12. EFFECT OF REWORK TIMES FUNCTION CHANGE ... 39
13. EFFECT OF RANDOM FAILURE CHANGE 40
14. EFFECT OF TRANSPORTATION TIME CHANGE .... 42
15. FACILITY EFFECTS WITH PF PROGRAM 43
16. 99% U.C.L. ON MEAN NUMBER OF ENGINES IN
THE REWORK FACILITY 45
17. MANAGEMENT POLICY EFFECTS 46
18. MANAGEMENT POLICY EFFECTS 47
19. DOLLARS VERSUS ENGINE WEEK LOST TRADEOFFS . . 52
20. ENGINE WEEKS LOST VERSUS REWORK FACILITY
CAPACITY BY PURCHASE PLAN 56
A-l. DISTRIBUTION OF MONTHS TO ACCUMULATE
6,000 HOURS AT SEA 61
A-2. DISTRIBUTION OF MONTHS TO ACCUMULATE
9,000 HOURS AT SEA 62
A-3. DISTRIBUTION OF MONTHS TO ACCUMULATE
12,000 HOURS AT SEA 63
A-4. REGRESSION OF TIME AT SEA ON CALENDAR
MONTHS 64
I. INTRODUCTION
The U.S. Navy has awarded a contract to Litton Industries
Inc. to build thirty gas turbine powered destroyers. These
ships, known as the Spruance or DD 963 class, are unique in
many respects. They will be built by a single contractor in
a new shipyard designed to employ the most advanced construc-
tion technology and mass-production techniques . Weapons sys-
tems will be off-the-shelf items but ample space, weight,
and electrical power margins have been designed into the ships
for future weapons systems modifications.
One of the unique features of the DD 963 class ships is
their main engines. These engines are General Electric
LM-2500 gas turbines, a marine version of the engine which
powers the Lockheed C5A transport aircraft. The ships have
been designed so that an engine can be removed and a new one
installed in less than twenty four hours. Except for a
crane, special equipment is not required by the ships crew
to effect an engine change. This allows the engines to be
designed for virtually no shipboard maintainence; conse-
quently, a substantial saving in manpower is realized.
Another result of this quick-change capability is that
shipyard periods are independent of engine life and can
therefore be scheduled at greater intervals.
Utilization of a quick-change capability requires the
maintainence of a rotable pool from which replacements for
high-time and failed engines can be drawn. This study, re-
quested by the DD 963 project manager, addresses the problem
of determining the pool size required to support a growing
fleet of turbine powered destroyers.
10
II. NATURE OF THE PROBLEM
A. GENERAL
DD 9 63 class ships will require a rotable pool of spare
engines as part, of the maintenance plan. Whenever an engine
installed in an operating ship fails or accumulates a
specified number of operating hours it will be removed from
the ship and sent to a rework facility to be overhauled.
The removed engine will be replaced by a new or previously
overhauled engine from a pool of ready for issue engines.
After the engine is overhauled it is stored in a ready for
issue condition until it is required to replace another
engine in the fleet.
The objective of this study is to determine the number
of engines, in addition to those installed in the ships,
required to maintain various levels of engine availability.
A secondary objective was to study the effect of the PF
program on pool size. The PF program, as proposed, includes
construction of 50 escort ships beginning in 1978, each of
which would have two LM-2500 engines, significantly in-
creasing engine population.
Figure 1 shows the flow of engines during the life cycle
of the DD 963 and PF class ships. This is the system which
was simulated to meet the objective of the study. It is
basically a closed loop system with two external inputs.
The construction schedules for DD 963 and PF class ships
introduce engines into the system, thus starting it opera-
tion. The purchase plans provide spare engines at various
11
NEWCONSTRUCTION
DD9671 PF
FLEET
SCHEI
OVHL!
TRANSIT
AIR SURF,
tip*
. Sci'ED. E1 OViL. V F.
EARLYrAILURE
TRANSIT
AIR SURF.
ROTABLEPOOL
PURCHASEPUN
REWORKFACILITY
IEXTRAREWORK
DELAYPRIOR TOREWORK
ENGINE FLOW PATHS
FIGURE 1
12
points in time to keep the system operating smoothly. With-
in the closed loop portion of the system, engines leave the
fleet when they fail, at scheduled overhaul, or at variable
scheduled overhaul depending on the operating philosophy in
effect at the time. The engines are then transported to the
rework facility for overhaul. When the engines arrive at
the rework facility they are either inducted into the facility
for overhaul or they wait for induction if the facility is
operating at capacity. They are then inducted when the fa-
cility can accommodate the additional engines . After the
overhaul is completed, the engines go to a storage location
(the rotable pool) until a requirement is generated by the
fleet. At that time, the engine is transported to the ship
requiring a replacement engine, thus completing the closed
loop system.
This system is similiar to a single echelon, repairable
item inventory system. However, this system differs from the
normal inventory models in that both supply and demand are
stochastic with supply dependent upon previous demand. In
standard inventory models, the objective is to develop
optimal decision rules to determine "when" and "how many"
items to procure during the operation of the system. Due
to the long budgeting and procurement lead times , the ob-
jective of this study is to develop information from which
the decisions of "when" and "how many" can be made prior
to the start of the system operation vice decision rules
for use during system operation.
13
B. ASSUMPTIONS
Several simplifying assumptions were made in order to
reduce the system to its essential elements. It was felt
that the assumptions made would not appreciably affect the
accuracy of the model.
The first assumption made was that all engines in the
fleet would accumulate operating hours independently. It
was felt that the largest part of any dependence which
existed in the system would be among engines on individual
ships. This dependence would possibly be different for the
various ships depending on their Commanding Officers * engine
operating policies . Computer programming problems as well
as a lack of knowledge about the nature of these relation-
ships made their inclusion infeasible. This assumption
should not significantly affect the results of the simula-
tion since sets of four engines are relatively small com-
ponents of a 120 engine population.
Another assumption made was that reworked engines are as
good as new. This implies that all engines entering the
fleet will be fully reworked and considered zero- time
engines. This eliminates the possibility of some engines
being selectively repaired and returned to the fleet with
a shorter time to overhaul.
It was assumed that ships will always have engines if
available. This assumption eliminates the possibility of
a ship's engines being removed at the start of a yard
period, being reworked, then returned to the same ship. If
14
an engine must be replaced, one is sent from the pool im-
mediately; if an engine is not available, the fleet is con-
sidered to be short one engine until one becomes available.
The entire engine assembly was considered as a single
entity by assuming that the gas generator and power turbine
had the same overhaul schedule. It was also assumed that
when an engine fails, both major components must be removed
and completely overhauled.
Random engine failures were assumed to be distributed
uniformly on the time interval from installation to scheduled
overhaul. This increasing failure rate distribution was con-
sidered to be more convenient than a truncated exponential
distribution. The exponential distribution was used only to
convert failure frequencies in the Maintenance Engineering
Analysis (MEA) to an estimate of the probability of an engine
failing prior to its scheduled overhaul.
Transportation time was assumed to include engine re-
moval and replacement time. For scheduled engine changes, it
was further assumed that engines would be shipped from the
pool to arrive in time for the change. Transportation time
includes time for old engine removal and shipment time to
the rework facility then to the pool. For random failures,
the replacement engine was delayed enroute to the ship for
a time equal to transportation time.
It was assumed that input rates were deterministic. The
function which loads ships into the GPSS program was derived
from planned ship launch dates, but can be changed easily.
15
The overhaul times used are estimates by officals at
Kelly Air Force Base of the time it would take to overhaul
the LM-2500 engine. Air Force estimates were based on
actual rework of a version of this engine, thus their esti-
mates were considered reliable. It was assumed that these
estimates would reflect all factors affecting the rework
time such as parts shortages, labor problems and accidents,
etc. It was further assumed that there would be only one
facility since it is not likely that the Navy will have
enough LM-2500 engines in the foreseeable future to justify
more than one.
16
III. THE MODEL
A. REASONS FOR SIMULATION
Preliminary analysis of the DD 963 inventory problem dis-
closed that system complexities rendered analytical modeling
infeasible. In view of this fact, a computer simulation was
determined to be the most promising form of analysis. Addi-
tionally, simulation offers the advantages that as data be-
comes available, the model can be updated to reflect "real
world" changes. Computer simulation further offers the
analyst the ability to vary key parameters across their
ranges of uncertainty, deriving in the process, worst, ex-
pected, and best case estimates.
B. MODEL DESIGN
A combination GPSS and FORTRAN model was developed, and
designed so that changes in system configuration could
easily be incorporated. Data gathered from the GPSS model
is fed onto a magnetic disk where it is stored until used
by the FORTRAN program. The advantage of this linkage is
that it frees the analyst from the intermediate step of
assembling the data to input the FORTRAN section. An ac-
companying disadvantage is that this disk linkup must be
altered slightly to conform to the features of the computer
system being used. Depending upon model configuration,
approximately one minute of computer time is needed to
simulate five years of system life.
17
C. GENERAL DESCRIPTION
The simulation was constructed in modular form to permit
the maximum amount of flexibility in modeling various states
of the system as well as in changing the output statistics
desired. There are two main and seven secondary sections in
the program. They are listed below and described in the
following sections.
1. GPSS Section
a. The base case consists of the basic simulation
with the DD 9 63 input.
b. The base case with the PF load allows the addi-
tion of PF engines to the base case.
c. Management options allow the extention of TBO
by some specified amount contigent upon rework facility load.
d. Purchase plan option allows the testing of
various purchase strategies to determine cost and expected
outages
.
e. The split rotable pool option allows the testing
of the effect of using two rotable pools.
f. The statistics section accumulates the data that
is desired from the GPSS program.
2. FORTRAN Section
a. SUBROUTINE READ reads the data from the disk to
input the FORTRAN program.
b. SUBROUTINE CLIM reads data provided by READ and
computes confidence limits on number of engines required.
c. SUBROUTINE COST calculates twenty year life cycle
costs of the rotable pool.
18
D. OPTIONS OF THE MODEL
1. Option 1
The primary model (option 1) consists of those com-
ponents which are necessary to mimic the DD 96 3 program.
Engines are delivered (zero-timed) into the fleet with the
launching of each ship. The engines then accumulate time
as a function of their operating schedule which is a "Model
Variable" (MV) . Engines may fail early with some probability
(MV) , or they continue in service until they accrue TBO , at
which time they are replaced. Engines replaced for either
reason are shipped to a single rework facility incurring
some transportation delay (MV) enroute. Upon arrival, they
wait for an opening; if the rework facility is operating at
less than capacity (MV) they are inducted immediately. Re-
work capacity is defined to be the number of engines which
can be in rework simultaneously. Once in rework, the engines
are overhauled, their rework time being a function of how
many LM-250 engines the facility has overhauled. Upon com-
pletion of overhaul, engines are then shipped to the rotable
pool with some transit time (MV) . Once in the rotable pool,
engines wait until they are demanded by the fleet. It
should be noted here that a large number of engines are pre-
loaded into the pool. In this way demand is always satisfied
and engine requirements may be measured as the number of
engines actually removed from the pool.
Engines which are replacements for those engines
which have failed unexpectedly travel from the rotable pool
19
to the fleet with some delay (MV) . The reworked engines then
commence the same cycle.
2. Option 1 With Patrol Frigate Program
Option 2 consists of the PF LOAD superimposed on
option 1. At some time after the launching of the DD 963
the patrol frigates engines arrive in the fleet at the rate
of two per month (MV) until the fiftieth PF launches. Any
number of PF's may be simulated, as well as any schedule.
3. Management Options
Option 3 differs slightly from Option 1, in that the
times at which engines may be replaced can now be controlled,
except for those engines which fail prematurely. Engines
which do not fail prematurely may be removed early or late
by some percentage (MV) of replacement time. Engines are
extended in-service contingent upon rework facility load.
If the load is less than some number of engines (MV) under-
going rework, then the engine is inducted. If facility load
is greater than that deemed appropriate for early induction,
the engine continues in service until either the facility
load drops, or the engine reaches TBO plus some percent of
TBO, i.e. TBO+10%. At this time, the engine is inducted re-
gardless of facility load. In this option, there is also
the capability of considering deployed engines. Some percent
(MV) of those engines not failing randomly are considered to
be on deployment. A deployed engine is extended the full
time allowed (MV) to permit completion of deployment without
changeout.
20
4. Purchase Plan Options
This option allows the testing of various buying
strategies in order to observe cost versus expected outage
results. The simulation flow is as described for option 1,
however, the rotable pool is now loaded according to some
purchase plan, and it is possible for the pool to become
empty. The number of engines bought each year must be
specified for this input. The simulation proceeds as be-
fore, with the addition of a section to gather statistics
on engine-weeks lost as a result of the particular purchase
plan being tested.
5. Split Rotable Pool Option
This option is basically that of option 1 with the
following proviso. There can be multiple pools, and they
may be drawn upon only by those engines in the fleet they
serve. In the two pool case - two fleets, operating inde-
pendently, are each served by their own pool, but use the
same rework facility. Additionally engines may not be
shipped between pools. The model was not extended past
two rotable pools.
E. MODEL OPERATION
The GPSS model is used to predict the 20 year life his-
tory of the engine inventory system. Statistics are gathered
every 8 weeks (MV) on the number of engines in the pipe-
line. By taking repeated observations at a particular
"time slice", the model obtains a distribution of the
number of engines needed as a function of time and the
21
model parameters being used. The mean and standard devia-
tion for all "time-slice" distributions are printed and the
resulting confidence intervals displayed graphically by
the computer. The result is the expected "history" of
that particular model which can then be compared with other
model versions to establish trends in model behavior.
A listing of the model parameters along with their de-
scriptions may be found in Appendix E.
The model structure of GPSS normally accumulates
statistics on key aspects of the system. These have been
suppressed as extraneous to the problem at hand. Such
statistics may be easily gathered to answer other "system"
questions. Example of possible model-extension statistics
are:
1. Average pipeline time (system)
.
2. Rework facility usage data.
3. Total transportation time.
Each distribution is based upon ten observations . De-
spite the loss of statistical accuracy, ten was determined
to be the maximum feasible number of observations to make.
System trends can clearly be distinguished at this level,
and the accuracy that could be provided by increasing the
number of runs does not warrant the required computer time.
F. LEVEL OF DETAIL
The model is not intended to reflect every detail of the
"real world" system. Thus, for example, no attempt was made
to maintain engine identity with its parent ship or shaft.
22
This would be a significant logic problem and the model
would become at least one order of magnitude more detailed —if the attempt were made to account for the statistical
dependence that will probably exist in the real world. As
a result, the assumption is made that the engine replace-
ments are independent. It is felt that the current model
can provide an adequate basis for analysis of major system
trends. More succintly:
"It is essential, therefore, to extract from thereal system those factors and relations whichhave a significant effect upon the performancemeasure being examined and to disregard all un-important details; keeping in mind, however,that what is deemed unimportant in one studymay have vast implications in another" [Ref . 1]
.
23
IV. PRESENTATION AND ANALYSIS' OF DATA
A. SELECTION OF THE BASE CASE
Due to the large number of variables in the problem, it
was impossible to examine them in every possible state of
nature. As a result, it was necessary to select an expected
case and observe the effects of key system variables upon
this "base case".
The system variables which follow are listed along with
their sources and are individually the "most likely value"
that the variable of interest will assume.
1. Fleet Operating Profile
The current operating profile of about 16 50 eng.
hrs/yr is assumed most likely. This information is derived
from Fleet Fuel and Steaming reports [Ref. 4] covering the
years 19 65 to 19 70.
2. Time Between Overhauls (TBO)
TBO is assumed to grow as specified in Figure 2.
This estimate is furnished by PMS-389
.
3. Rework Time
Overhaul time of the engines is expected to follow
the learning curve in Figure 3. This estimate is furnished
by officals at Kelly A.F.B.
4. System Transit Tine
It was assumed that these engines would be individ-
ually-managed high priority items. A mean system transit
time of three weeks was assumed.
24
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5. Probability of a Random Failure
This percentage was derived from Litton' s Maintenance
Engineering Analysis (MEA) [Ref. 3] assuming a TBO of 60 00
hours. A figure of 13.5% was obtained (Appendix C) . Thus
13.5% of the operating engines are expected to fail prior
to TBO.
6. Rework Capacity
Rework capacity was selected as four, i.e. four
engines may be undergoing overhaul simultaneously. This is
roughly the mean number of engines requiring rework in one
26
month without the load from the PF program. Four is not
the most likely number for rework capacity, but rather the
smallest value that can meet the base load requirements.
In this respect, the base case is pessimistic.
B. NATURE OF RESULTS
Figure 4 is a plot of base case spare engine require-
ments at upper confidence limits of 99%, 95%, 85% and 75%
as drawn by a computer operated plotter. All other figures
show only 99% confidence levels. All confidence levels
are calculated using the results of ten observations of
system requirements and assuming that observations are
distributed normally (Appendix D)
.
The number of spare engines required throughout the
twenty year system life appears to be cyclic in nature
with requirements, in most cases, rising to a global
maximum near the three hundredth week of system life
(fiscal year 1981). After the global maximum, require-
ments rise and fall in a cyclic manner. The magnitude
and time of the various extreme points depend on the
values of the input variables
.
Figure 5 shows the base case (99% confidence limit)
requirements from four series of runs of the simulation,
each ten-run series made with a different random number
seed. The coincident nature of the four plots indicates
that the choice of random number seed will not signifi-
cantly affect the results of the simulation.
27
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The global maximum near week 300 appears to be caused
by overlaping engine requirements. The first ships launched
require engines for their second overhaul at the same time
the last ships require engines for their first overhaul.
As time progresses past F.Y. 19 83 (week 400) , the maximum
and minimum requirements become less extreme due to the ef-
fects of the random variables in the system.
C. EFFECT OF CONSTANT TBO'S
The first variable investigated was the time between
overhauls. Figure 6 illustrates the effect on 99% upper
confidence limits of varying TBO over the values of 4,0 00,
6,000, 8,000 and 10,000 hours in the case where ships
operate in a manner similar to present day destroyers.
As the TBO increases, the number of engines required de-
creases and the time at which the maximum demand occurs
is later. If the TBO is as short as 4,0 00 hours, the num-
ber of spare engines needed is significantly increased.
The maximum is ten engines greater than with a 6,000 hour
TBO.
The effects of the same four TBOs were investigated
in the cases of ships operating 2,000 and 2,500 hours per
year (Figs. 7 and 8). As expected, increasing TBO de-
creased the number of spare engines required. If the
engines are operated 2,000 or more hours per year and
TBO is 4,000 hours, the rework facility becomes saturated
and can not overhaul engines as fast as they are demanded.
30
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This condition exists even beyond the time when engine
requirements should be expected to decrease.
D. EFFECT OF TBO GROWTH
A TBO growth function is incorporated in the base case.
This function is considered to be a reasonable guess of
how TBO can be expected to increase with system life. The
base case growth function and three others are shown in
Figure 2. These functions were used to modify the current,
2,000 hour and 2,500 hour yearly operating time simulations.
Results are presented in Figures 9, 10, and 11. Since the
base case results fell between the other results in Figure
9, they were omitted for reasons of clarity. In the case of
ships operating as they do now, the various TBO growth
functions have very little effect. The difference in global
maxima is only three engines. It can be seen in Figures 10
and 11 that, at an increased tempo of operations, a signifi-
cant reduction in the number of engines required is achieved
if the slightly better TBO growth rate is realized. This
growth rate (TBO increases starting one year earlier than
in base case) results in reductions of five and ten engines
at 2,000 and 2,500 hours per year operating rates respectively
There is, however, an unexpected anomaly in Figure 10. The
global maximum for the one year late growth rate case is
almost four engines higher than expected. This was due to
the higher than usual variance between observations near
week 300. Another ten runs were made with a different ran-
dom number seed and results almost coincident with the
34
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"on time" TBO growth function in Figure 10 were observed.
There were no other cases in this study where this phe-
nomenon was observed.
E. EFFECT OF REWORK TIMES
The base case rework time is assumed to be a step
function (Fig. 3) in which the mean rework time is deter-
mined by the number of engines which have passed through
the overhaul facility. Figure 12 illustrates the effect
of varying the magnitude of this function. It can be seen
that if rework time is taken as in the base case or one
week less, the results are almost identical. When the
overhaul time was one week more than in the base case, the
maximum number of spare engines needed increased by three.
When it was two weeks more, the spare engine maximum re-
quirements increased by fifteen. This result was obtained
utilizing a facility with a capacity of four engines. It
is felt that a larger rework facility would significantly
reduce the effect of these longer rework times.
F. EFFECT OF RANDOM FAILURES
The simulation was run with the probability of random
failure changed to .085, .185, and .235 from the base case
value of .135. There was little difference in results,
therefore only the two extreme cases were plotted in
Figure 13. It can be seen that the model is relatively
insensitive to changes of the probability of random failure
in the range .0 85 to .235. The maximum number of spare
38
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engines required actually decreases as more random failures
are encountered. This is because the global maximum occurs
when a large number of ships arrive for scheduled engine
overhaul in a short period of time. Increasing random fail-
ures causes engines to fail prior to this time, thus fewer
scheduled changes are required at the time of peak demand.
G. EFFECT OF SYSTEM TRANSPORTATION TIME
The base case with mean transportation time of three
weeks was compared to runs made with times of two, four
and five weeks. As expected, increasing transportation
time increases the number of spare engines required.
Since the increases were small, only the extreme values
were plotted in Figure 14. The difference in global
maxima for the two week and five week transportation time
cases was three engines.
H. EFFECT OF PF PROGRAM AND REWORK FACILITY CAPACITIES
The effect of including the PF program in the simulation
is to cause a global maximum of thirty one engines to occur
at the six hundredth week of system life (F.Y. 1987) . This
maximum is large because the rework facility becomes satu-
rated and cannot overhaul enough engines to satisfy the
additional demand imposed by the PF engines. Figure 15
shows that this effect may be largely eliminated by in-
creasing the capacity of the facility to seven engines.
This increase reduces the maximum number of engines re-
quired by sixteen. A facility with a capacity of ten
41
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engines offers no substantial additional savings of spare
engines. The reason for this can be seen in Figure 16
which shows that mean rework facility load (9 9% U.C.L.)
never went above seven engines with a facility capacity of
ten.
I. EFFECT OF MANAGEMENT OPTION
Figures 17 and 18 show the effect of allowing engines
to operate up to 10% beyond scheduled overhaul time if the
rework facility load is four engines. It can be seen
(Fig. 17) that if the facility capacity is seven engines,
this policy offers little advantage. A significant saving
of eight spare engines is realized (Fig. 18) if a small
four engine capacity facility is used.
J. BASE CASE ENGINE REQUIREMENTS
Table 1 shows the fiscal years in which additional
engines were required for the DD 96 3 program and their
relative costs as a function of time between overhauls and
the operating tempo of the ships. These are results when
the simulation is run with a sufficient number of engines
in the pool to preclude not having one available when de-
manded. The figures in Tables I and II , are the annual
incremental increases of the number of engines needed from
the pool to meet demand. These figures are 95% upper con-
fidence limit of the mean. Rework time, percent early
failure, transportation time, and rework facility capacity
of the base case were utilized in all runs tabulated in
Tables I and II.
44
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49
Review of this data reveals that the engine requirements
are relatively insensitive to time between overhauls when
the TBO is 8,0 00 hours or more. The very large number of
engines required for a TBO of 4,000 hours and operating
levels of 2,0 00 and 2,500 hours per engine per year can
attribute to the limited rework capacity as previously
noted.
K. EFFECTS OF VARIOUS PURCHASE PLANS
After the general operating characteristics of the sys-
tem were learned, several sample purchase plans were tested
to determine expected engine weeks lost and the associated
cost. In each purchase plan tested, it was assumed that
the engines were paid for and delivered at the start of the
fiscal year indicated. The purchase plans tested along
with their results are shown in Table III. Engine weeks
lost is a time weighted backorder measure of system ef-
fectiveness. It was assumed that a shortage of one engine
for two weeks was equivalent to the shortage of two engines
for one week in degredation of system effectiveness. All
purchase plans were tested with the parameters of the base
case.
As expected, purchase plans for more engines and earlier
purchase dates resulted in lower numbers of engine weeks
lost and correspondingly higher costs. Figure 19 is a plot
of engine weeks lost versus total discounted costs. The
numbers on Figure 19 refer to purchase plan numbers in
Table III. The curve plotted on Figure 19 is an efficiency
50
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52
frontier for the system, i.e. each point on the curve repre-
sents the least cost purchase plan strategy for a given num-
ber of engine weeks lost. Figure 19 also illustrates which
plans are dominated (more expected engine weeks lost for
more doHare ) ; for example, plan 16 is dominated by plan 15.
The slope of the two straight lines indicate the trade-
off rate between engine weeks lost and dollars. A projected
cost of $25,0 00 per day or $175,0 00 per ship week was used
in the determination of the slope of these lines. The 10%
line assumes the lack of one engine decreases a ship's
capability to complete its mission by 10% and the 100% line
assumes the lack of one engine causes the ship to lose all
capability to complete its mission. Thus, in this case,
the decision lies between the two points of tangency,
roughly 12 to 15 engines in the rotable pool. The optimal
purchase plan depends on the cost of having a ship without
an engine for one week. Thus the optimal number of engines
in the pool is that number of engines for which the cost of
an additional engine is greater than the savings that result
from reducing the engine weeks lost.
Also significant, is the fact that plans 21 through 27
resulted in increased costs but no decrease in the expected
number of engine weeks lost. This implied that there were a
sufficient number of engines in the pool to have one avial-
able whenever a demand was generated and that the only time
the fleet was short an engine was during the time required
to transport and install an engine which was a replacement
53
for an early failure. Engines for scheduled changes are
assembled to be shipped sufficiently in advance to be avail-
able when the old engine is removed from the ship. Also
implied is that there is no increase in pool size which
would eliminate transportation and installation time loses
for early failure engines.
Five purchase plans were tested to determine if in-
creasing rework capacity in lieu of buying more engines
would reduce the engine weeks lost. The result of the
increased rework capacity is shown in Table IV. The results
of four of the plans are plotted in Figure 20 with base case
rework facility capacity indicated. Plans 21 and 22 resulted
in no significant differences in engine weeks lost at any
rework facility capacity. The faility capacity affected the
engine weeks lost when a purchase plan with a lower number
of engines was tested. This illustrates the existence of a
cost tradeoff between rotable pool size and rework facility
size. It was possible to obtain the same minimum number of
engine weeks lost with plan 21 for 15 engines and a rework
capacity of four, and plan 19 for 14 engines and a rework
capacity of eight. The decision here would depend on the
cost of adding an additional engine to the rotable pool and
the cost of increasing rework facility capacity.
54
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56
V. CONCLUSIONS
1. Rotable pool requirements are most heavily dependent
upon rework facility capacity, i.e. that number of engines
which can be in rework simultaneously. Any condition which
will produce an engine removal rate from the fleet of about
40 engines per year is sufficient to saturate the facility
(facility capacity=four)
.
In particular, the PF program requires 33 engines in
the pool if capacity is four. This requirement decreases to
16 if the capacity is greater than seven engines . Little fur-
ther improvement is observed for capacities larger than seven,
2. The effect of increasing operating schedule is com-
parable to that of decreasing TBO. Again, the engine re-
moval rate will determine if facility capacity is sufficient.
Any operation schedule/TBO combination yielding a removal
rate of 40 engines a year will drive pool engine require-
ments above 20, other parameters held at base case levels.
3. TBO growth rates (Fig. 2) have little effect on
rotable pool size with current operations. The best to
worst case differential is three engines. Increasing the
operating tempo to 20 00 engine hours per year will result
in an engine requirement differential of eight engines. If
operating hour requirements increase to 2500 hours per year,
then the best to worst case difference in TBO growth will
yield a difference in engine requirements of 15.
4. Increasing mean rework time by two weeks across the
entire learning curve will result in additional requirements
57
of 16 engines, whereas an average one week increase results
in only four additional engines being required over the
base case. Base case requirement are for 12 engines. A
decrease of one week across the learning curve does not
affect system requirements. This is due to the fact that
the rework time is bounded below at 25 days and during the
portion of time when the rework time decrease is effective,
system load is light.
5. The percentage of operating engines failing randomly
is not critical to the system in the range 8.5% to 23.5%.
6. System transit time is significant to the extent
that one additional week in transit will require a rotable
pool increase of about one engine.
7. Extensions of TBO by ten percent contingent on re-
work facility load levels have significant potential if the
rework capacity is small (four engines) . Extensions have
little effect at the higher facility capacity levels.
8. For the base case assumptions with rework capacity
variable, system effectiveness is optimized for a rework
capacity of 7-8 engines and the purchase of 14-16 engines
early in system life as rotable pool spares, depending
somewhat on the cost of the rework facility.
58
VI. KECOMyLENDATIONS
1. Acquire and analyze available cost/time data for
probable transportation systems. Optimum system transit
time can then be computed.
2. Acquire and analyze ship operating profiles to de-
termine which overseas stock points are prime candidates
for possible stockage for random failures. Once prime
stockage locations have been identified, transportation
cost/time data can be used to determine if overseas stocking
should be used. Since most engine failures can be expected
to occur while the ship is at sea, consideration should be
given to the possibility that a spare engine can be trans-
ported to the installation point prior to the arrival of the
ship. If this were done, prepositioning would not further
reduce lost engine time.
3. Determine the effect of sets of engines arriving
for rework simultaneously.
4. Determine cost of rework facility at various capac-
ities to evaluate possible pool size/rework facility
capacity tradeoffs
.
59
APPENDIX A
DISTRIBUTION OF TIME BETWEEN SCHEDULED OVERHAULS
Data on destroyer operations was obtained from the Navy
Maintenance and Material Information System, Steaming,
Operating, and Fuel Listing dated 20 August 19 71 [Ref . 4]
,
which lists the number of hours each destroyer type ship
was underway each month from July 19 65 through April 19 71.
It was assumed that the DD 963 class destroyers operating
schedules will be similiar to the current schedules of a
destroyer (DD) , a guided missile destroyer (DDG) , or a
guided missile frigate (DLG) . The monthly hours at sea
were totaled for each ship until totals of 6,0 00, 9,0 00
and 12,000 hours at sea were accumulated to determine the
number of calendar months it took to accumulate the
specified number of hours. Linear interpolation was used
to determine what poriton of the final month was required
to reach the desired total number of hours.
From these totals by ship, three histograms (Figs.
A-l, A-2 and A-3) were drawn to determine the distribution
of calendar months to reach a specified number of hours
at sea.
Three least squares regressions were performed on the
mean, maximum, and minimum times to accumulate 6, 9, and
12 thousand hours at sea to predict the calendar months
required for a specified number of hours at sea. Figure
A-4 shows the actual data points and the three linear
regression lines. From Figure A-4 it was assumed that the
60
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63
1 2 3 4 5 6 7 8 9 10 11 12 13TIME AT SEA( THOUSANDS OF HOURS)
REGRESSI ON OF TIME AT SEA ON CALENDAR MONTHS
FIGURE A-4
64
maximum, minimum, and mean calendar months are linear func-
tions of the number of hours at sea. It was also assumed
that the distribution of months to 12,000 hours at sea was
representative of the distribution of time at sea for a
destroyer type ship. Time at sea was converted to time per
engine using the assumption, supplied by PMS-389, that 96%
of all operations will be using two engines and 4% of the
time four engines will be operated.
Utilizing the linearity and distribution assumptions
noted above, a computer program was written which predicted
the maximum and minimum months between engine overhauls and
distributed all overhauls between these figures in a
smoothed version of the 12,0 00 hours at sea histogram. The
output of this program produced distribution function inputs
for use in the GPSS simulation program.
A further assumption was that if DD operations tempo
was varied, the distribution of months to accumulate a
specified number of hours varied linearily. Thus the same
computer routine was able to generate distribution function
inputs for the simulation of various levels of destroyer
operation and TBO's.
65
APPENDIX B
COSTING INFORMATION
A computer subroutine was written to estimate the cost
of various purchase plans. The cost figures developed in
this study cannot be considered solid figures for budgeting
purposes, but only relative costs of various purchase plans
to assist in evaluating various purchase strategies. The
only costs considered in this study are holding and purchase
costs. A cost estimate of $800,000 for the initial spare
engine delivery was received from PMS-389. To this figure
a cost escalation of 5% per year was assumed to determine
the cost of an engine in succeeding time frames
.
The standard inventory theory premise that holding cost
is a percentage of the purchase cost was utilized in this
study. This holding cost is considered to contain three
components. The first component is the actual cost of
storing the engines when they are waiting demand from the
fleet, including such factors as administrative costs,
possible deterioration of the engines from nonuse, packing
and preservation costs, cost of the storage facility, etc.
The second component of holding cost is the cost associated
with investing funds in engines vice other uses. Funds in-
vested in unused engines are not available to meet any
other needs of the Navy. The third component is obsolescence
cost. This is the cost of making alterations to engines
after purchase due to technological improvements. It is
66
assumed a new engine would be built with all improvements
developed up to its construction time incorporated into it,
thus the alterations would be required only for previously
built engines. A holding cost equal to 12% of the total
purchase price per year, as set by PMS-389, was used for
all cost estimates in this study.
Annual costs are computed for each year through fiscal
year 19 94, i.e. twenty years from the scheduled delivery of
the first ship. After computation of the yearly costs,
system inventory costs are computed. Total system inventory
costs are discounted to 19 72 dollars using a discount rate
of 7.75% per year to enable better comparisons of various
purchase plans.
The cost subroutine can be utilized in two modes. In
the first application, it is used as a subroutine to the
system simulation. In this mode, the subroutine receives
as inputs the number of engines required to achieve a
specified confidence of having an engine when one is re-
quired by the fleet. This is utilized whenever the simu-
lation is run with an unconstrained number of engines.
Whenever the simulation demonstrates a need for more engines,
than previously required, the purchase cost of the additional
engines is computed based on the year in which it is re-
quired. All engines purchased are maintained in the rotable
pool for the remainder of the system life, even if the
simulation shows that fewer engines would be required at
a later period of time.
67
In the second mode, the subroutine costs predetermined
purchase plans over the life cycle of the ship system in-
dependent of the actual system requirements. The costing
of predetermined purchase plans allows comparison of cost
to engine weeks lost when the simulation is run in a con-
strained pool size mode.
The costing subroutine uses initial engine cost, holding
cost rate, and discount rate as variable input parameters..
This feature allows future testing to determine the change
in relative costs as these values are varied.
68
APPENDIX C
[RELIABILITY CONSIDERATIONS
Since the DD 96 3 class destroyers have not yet been
built, good data on engine reliability is not available.
An estimate of the order of magnitude of the engine reli-
ability was obtained from the Maintenance Engineering
Analysis [Ref. 3] prepared by Litton Industries, which
contains estimates of failure frequencies for various
engine components
.
Table C-I lists the components which, if they fail,
will require an engine to be changed. The failure
frequency for each component is the number of failures
expected in one year of operation based on 2,500 engine
hours/year. In the M.E.A., all engine components were
assumed to have an exponential failure distributions,
thus the failure frequencies for critical components
(Table C-I) could be added. The sum of these frequencies
can then be converted to an engine removal rate (removals/
hour) as follows:
Failure FrequencyRemoval Rate (RR) =
2500
The probability of an engine having to be removed in
some time interval (T) is:
Pr(R) = l-exp(-RR x T)
59
COMPONENT FAILURE FREQUENCY(Failures/Year)
A. Gas Generator
1. Compressor front frame 0.00122. Compressor rotor 0.00183. Compressor stator assembly 0.004574. Compressor rear frame 0.00125. Main bearings 0.02106. Combustor 0.00407. High pressure turb . rotor 0.01228. High pressure turb. stator 0.00249. Turbine mid- frame 0.00469
B. LP (Power) Turbine
1. LP (power) turbine 0.0024rotor assembly
2. LP (power) turbine 0.0037stator assembly
3. LP (power) turbine 0.0012rear frame
FAILURE FREQUENCIES FOR CRITICAL COMPONENTS
TABLE C-I
It was desired to know the probablity of an engine having
to be removed prior to its scheduled overhaul time, therefore
(T) in the above equation was taken as TBO. These prob-
abilities are tabulated in Table C-II for various TBO's.
EARLY FAILURE PROBABILITIES
TBO Pr(R)
4,000 .092
6,000 .135
8,000 .176
10,000 .215
12,000 .252
TABLE C-II
70
Instead of assuming that the given failure frequencies
were true and then using the Pr(R) corresponding to each
TBO, the value for 6,0 00 hr (.135) was used in the base
case and the simulation was tested for sensitivity to
changes in this value. This implies that as TBO increases,
failure frequency decreases in the simulation.
71
APPENDIX D
NORMALITY OF RUNS
The simulation was run ten times for each choice of
variables and the number of spare engines required at each
point in time was tabulated after each run. The GPSS pro-
gram calculated the mean and standard deviation of number
of engines at each point in time. In order to determine
confidence limits on these results, it was necessary to
assume some distribution. Since the data appeared to be
normal, a Kolmogorov-Smirnov test against the Normal
Distribution was made for several large samples. The
null hypothesis that the number of engines required at
various points in time is normally distributed could not
be rejected for a significance level of 0.0 5 in any case.
For samples taken beyond 10 weeks of system life, the
null hypothesis could not be rejected for significance
levels as high as 0.6.
72
APPENDIX E
DETAILED MODEL DESCRIPTION
A. CONTROL INFORMATION
The primary variables which may be altered in order to
establish the nature of the simulation model are:
NRUNS
NTIME
INCRE
START
RAND
TRANS
NPOOL
OPER
LEARN
LOT
PFLAG
LOADj
TIMEj
DPLOY
PCNTM
Number of observations/interval. Numberof START/CLEAR cards
.
Number of time intervals of interest.
Interval between time-slices.
Delay in starting statistical accumulation,
Percentage of random failures.
Transportation delay, includes shippingship to ship.
Number of engines loaded initially.
Holds function number which sets TBOgrowth or replacement time dist. to beconsidered.
Function which established rework facilitylearn ing curve
.
Number below which the number of enginesundergoing rework must fall to allow anengine to be induced early. OPTION 3
Delay of the PF program over launching ofDD 96 3. OPTION 2
Number of engines to be loaded in the jthload. OPTION 4
Time delay prior to loadj . OPTION 4
Percentage of ships on deployment whoseengines must be extended. OPTION 3
l/PCNTM=Percentage of TBO which an enginemay be extended. OPTION 3
FAC STORAGE JJ Capacity of rework facility is JJ.
73
JJ FUNCTION Function JJ contains replacement time forTBO and operating schedule. (Held inSAVEVALUE OPER)
SHIPS Function which determines delivery scheduleschedule of DD's.
DIFF Variable which measures number of enginesin pipeline.
RMULT Contains the seed of the random numbergenerators used.
J FUNCTION Contains the TBO growth rate to be used.
The basic time step for this model is one week. This implies
that all operations transpire in units of integer weeks.
If finer detail is needed the basic time step may be altered
by changing seven-ten cards in the main deck.
B. ACCUMULATION OF STATISTICS
Statistics are accumulated for NTIME(120) periods each
run for NRUNS(IO) runs. Interval between "looks" is INCRE(8)
weeks. General logic flow is contained in the flow charts.
C. INDIVIDUAL BLOCK DESCRIPTIONS
Detailed explanations of the individual GPSS instructions
are contained in the GPSS User's Manual [Ref. 2],
D. SUPPORTING FORTRAN SUBROUTINES
General logic flow for the fortran subroutines is con-
tained in Appendix G.
74
APPENDIX F
ACCURACY OF THE MODEL
During preliminary runs, much use was made of the TRACE
and PRINT block options of GPSS. These blocks enable the
analyst to chart carefully the transaction's progress through
the model, as well as observing the values of key savevalues
and parameters. Extensive use was made of the current events
chain to verify proper information storage. Examination of
the information thus proviced indicated that the model was
performing as intended.
In an effort to establish the basic correctness of the
model, a completely deterministic system was simulated by
hand. The results of this nonstochastic hand simulation
were compared to the model results with all stochastic ele-
ments removed. The results compared very favorably.
75
APPENDIX G
MODEL FLOW CHART
OPTION I
BASE CASE
IE/initialize
vvariables/_
^CREATE SHIPS
ACCORDING TO
SCHEDULE
CREATE FOUR
ENGINES/SHIP
ENTER
FLEET
DETERMINE TIME
FOR FAILURE OR
REPLACEMENTTRANSPORTATION
DELAY
ieplacemen;
random age replacement
\ 1/
OPERATE FOR
DETERMINED TIME
ILEAVE FLEET
DEMAND ENGINE FROM
ROTABLE POOL
TYES
TRANSPORTATION
DELAY
ENTER FACILITY
IF AVAILABLE
F NOT WAIT
WAIT FOR OVERHAUL
TIME
LEAVE FACILITY
TRANSPORTATION
DELAY
WAIT IN ROTABLE
POOL UNIT
DEMANDED
~^ZIS DEMAND FROM
A RANDOM FAILURE ?
NO
.INITIALIZE
^VARIABLES,
•"
CREATE CREATE SHIPS
PF'S ACCORDING TO
SCHEDULE SCHEDULE
< FIRST >\SHIP^YES
^ f ^f\iOCREATETWO CREATE FOUR
ENG/SHIP ENGINES/SHIP
EN ER
FLEET
DETERMINE TIME
FOR FAILURE OR
REPLACEMENT
^REPLACEMENT
7^%
OPTION HBASE CASE WITH PF'S
TRANSPORTATION
DELAY
RANDOM. AGE REPLACEMENTX —y-—OPERATE FOR
DETERMINED TIME
LEAVE FLEET
DEMAND ENGINE FROM
ROTABLE POOL
YES 4-
TRANSPORTATION
DELAY
ENTER FACILITY
IF AVAILABLE
IF NOT WAIT
WAIT FOR OVERHAUL
TIME
LEAVE FACILITY
TRANSPORTATION
DELAY
WAIT IN ROTABLE
POOL UNIT
DEMANDED
-IS DEMAND FROM
A RANDOM FAILURE?
NO
77
OPTION IE
MANAGEMENT
OPTIONS
SAME AS OPTION I
YES
OPERATE TILL
FAILURE
YES
EXTEND
TBO
ENTER FLEET
DETERMINE TIME
FOR FAILURE OR
REPLACEMENT
NO
OPERATE FOR
SOME PERCENTOF TBO
SHIP DEPLOYED?
» LEAVE FLEET
RANDOM FAILURE
DEMAND ENGINE
(REJOIN OPTION I)
NOLOOP FOR PERCENT
OF TBO
FACILITY LOAD.
^ LIGHT 1'
YES
NO
76
OPTION nTESTING OF PURCHASE PLANS
OPTION I
WAIT IN POOL
TILL ENGINE
DEMANDED
.Initialize
WARIABLESy
LOAD ACCORDING
TO SCHEDULE
STATISTICS SECTION FOR OPTION II
COUNT
SHORTAGESYES
a'
s-J
TABULATE
ENGINE WEEKS
OUT
<%
OPTION ISPLIT ROTABLE POOL
INITIALIZE
^VARIABLES/
("CREATE SHIPS
ACCORDING TO
.SCHEDULE _J
YF,A LOAD/
V
..CREATE FOUR.
ENGINES/SHIP
ASSIGN SHIPS
TO FLEET* 1 OR #2
ENTERFLEET #1 #2
DETERMINE TIME
FOR FAILURE OR
REPLACEMENT
TRANSPORTATION
DELAY
RANDOM
S.
REPLACEMENT
AGE REPLACEMENT"7
YES +
OPERATE FOR
DETERMINED TIME
LEAVEtti *o
FLEET & 1 * 2
DEMAND ENGINE FROM
ROTABLE POOL#1 fr2
TRANSPORTATION
DELAY
1ENTER FACILITY
WAIT FOR OVERHAUL
TIME
ILEAVE FACILITY
TRANSPORTATION
DELAY
i
'
WAIT IN ROTABLE
POOL UNTIL #1DEMANDED
#2
IS DEMAND FROM
A RANDOM FAILURE ?
NO
GPSS STATISTICS SECTION (GENERAL)
1C START RUN
J*-
WAIT FOR START TIME
WAIT FOR INCRE TIME
SAVE NUMBER OF
ENGINES NEEDED
RUNS COMPLETE ?
NO
81
SUPPORTING ROUTINES
SUBROUTINE READ/CONF
READ DISK TO
FIND DATA OF
INTEREST
READ DATA
READ INPUT
PARAMETERS
WRITE INPUT
PARAMETERS
CALL SUBROUTINE
CONFIDENCE LIMIT
RETURN
CPMUTE CONF
LIMITS
PLOT CONF LIMITS
CALL SUBROUTINE
COST
I
RETURN
82
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105
LIST OF REFERENCES
1. Goodman, R. M. and Pivonka , L. M. / A' Simulation Study• of the' Time-Sharing Computer System at the Naval• Postgraduate School , U.S. Thesis, Naval PostgraduateSchool, Monterey, California, June 1969.
2. Internation Business Machines Corporation FormH20-0326-2, General Purpose Simulation System/36User's Manual , 19 67.
3. Litton Ship Systems, LM- 2500 Propulsion Gas TurbineMaintenance Engineering" Analysis Record, 1 DecemberTTH7.
4. Navy Maintenance and Material Information System,Steaming, Operating and Fuel Listing, 20 Augusti57i:
106
INITIAL DISTRIBUTION LIST
No. of Copies
1. Defense Documentation Center 2
Cameron StationAlexandria, Virginia 22314
2. Library, Code 0212 2
Naval Postgraduate SchoolMonterey, California 9 39 40
3. Chief of Naval Personnel 1PERS-llbDepartment of the NavyWashington, D. C. 23070
4. Naval Postgraduate School 1
Department of Operations Researchand Administrative Sciences (Code 55)
Monterey, California 9 39 40
5. Asst. Professor J. K. Hartman 1
Code 55 (thesis advisor)Department of Operations Research
and Administrative SciencesNaval Postgraduate SchoolMonterey, California 9 39 40
6. Asst. Professor A. R. Washburn 1
Code 55 (thesis advisor)Department of Operations Research
and Administrative SciencesNaval Postgraduate SchoolMonterey, California 9 39 40
7. Assoc. Professor M. G. Sovereign 1
Code 55Department of Operations Research
and Administrative SciencesNaval Postgraduate SchoolMonterey, California 9 39 40
8. Assoc. Professor D. A. Schrady 1
Code 55Department of Operations Research
and Administrative SciencesNaval Postgraduate SchoolMonterey, California 9 39 40
107
9. Naval Ships Systems Command ID
Washington, D. C. 20 36Attn: PMS-389
10. Naval Ships Systems Command 1Washington, D. C. 20 350Attn: SHIPS 046
11. LT John S. Cushing, USN 1133 Gullott DriveSchenectady, New York 12306
12. LT William K. Gautier, USN 2
3703 Halls Ferry RoadVicksburg, Mississippi 39180
13. LT Douglas A. Long, SC , USN 1412 Ives AvenueBig Rapids, Michigan 49 30 7
Ik, Mr. Eugene P. Weinert, Head 1Combined Power and Gas Turbine BranchNaval Ship Engineering CenterPhiladelphia DivisionPhiladelphia, Pennsylvania 19112
108
Security Classification
DOCUMENT CONTROL DATA -R&D(Security classification of title, body ol abstract and indexing annotation mu.sf be entered when the overall report Is classified)
I ORIGINATING ACTIVITY (Corporate author)
Naval Postgraduate SchoolMonterey, California 93940
Zm. REPORT SECURI TV CLASSIFICATION
Unclassified2b. GROUP
3 REPORT TITLE
A Simulation Study of the LM-2500 Gas Turbine Engine Inventory System
4. DESCRIPTIVE NOTES (Type of report and.inclusive dates)
Master's Thesis; March 19725 au THOR(S) (First name, middle initial, last name)
John Scott Cushing; William Kirten Gautier; Douglas Allen Long
6. REPOR T D A TE
March 1972
7a. TOTAL NO. OF PAGES
110
76. NO. OF REFS
»«. CONTRACT OR GRANT NO.
b. PROJEC T NO.
9a. ORIGINATOR'S REPORT NUMBERIS)
9b. OTHER REPORT NO(S) (Any other numbers that may be assignedthis report)
10 DISTRIBUTION STATEMENT
Approved for public release; distribution unlimited.
II. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY
Naval Postgraduate SchoolMonterey, California 93940
13. ABSTR AC T
LM-2500 gas turbine engine rotable pool requirements were studiedusing computer simulation. System operating characteristics wereobserved with various scenarios and management philosophies. Severalpurchase plans were formulated and tested once system trends wereestablished. From this information, cost-effectiveness relationshipswere derived.
Best estimates of system variables indicated that cost-effective-ness was optimized for a rework capacity of seven to eight engines andthe purchase of fourteen to sixteen engines early in system life asrotable pool spares.
DD "«" 1473I NOV 83 I ™T / WS/N 0)01 -807-681 I
(PAGE 1)
109Security Classification
4-31408
Security Classification
KEY WO ROS
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01 -807-68? I
1473 (BACK
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